Motion and Resistance of a Low-Wat erp lane Catamaran 



If the effective hull form is to be chosen from a group of 

 existing monohull forms with good resistance qualities, the one with 

 the lowest resistance value at design condition is not necessarily the 

 best choice for the effective demihull form. The one with the lowest 

 resistance at the design speed may not give the best wave cancella- 

 tion between the two demihulls. The wave cancellation at a given 

 Froude number and a given hull distance depends upon the free wave 

 amplitude -spectrum distribution of each demihull. The wavemaking 

 resistance of a catamaran depends not only upon the level of the free 

 wave amplitude curve, but also upon the shape of such a curve. Befo- 

 re the best choice can be made, it is necessary to obtain the ampli- 

 tude-spectrum curve of each monohull, either experimentally or 

 theoretically. Experimental methods are available for obtaining 

 wave "cuts" from which a wave amplitude -spectrum curve can be 

 deduced. By using the Douglas program and the existing wavemaking 

 resistance theory, the wave amplitude -spectrum curve of a monohull 

 can also be computed. If the possibility of obtaining the wave ampli- 

 tude-spectrum curve does not exist, hull forms with pronounced 

 hollows and humps in their C p curves should be avoided, even 

 though the C r values at the design speed are relatively low. 



If a theoretical approach is used in designing an effective 

 hull form, two singularity distributions, one for each demihull, are 

 placed the desired distance apart. On the basis of linearized wave- 

 making resistance theory, the surface wave of a catamaran is a li- 

 near superposition of the waves produced by the demihulls. Within 

 the constraints of design conditions, the optimum singularity distri- 

 bution is obtained by minimizing the wavemaking resistance of a 

 catamaran. The final design, of course, has to be chosen on the 

 basis of total resistance rather than on the basis of wavemaking 

 resistance alone. By tracing a number of streamlines generated by 

 one of the singularity distributions in a uniform flow, the hull geome- 

 try of an effective hull is obtained. 



Based on theoretical insight and whatever practical informa- 

 tion is available, we assume that the design of an effective hull for a 

 demihull can be carried out successfully. Our remaining task is to 

 find a way of obtaining the geometry of a demihull from the geometry 

 of its effective hull form. This will be discussed in the next section. 



Developing the Geometry of a Demihull from its Effective Hull Form. 



Before discussing the procedure for obtaining the geometry 

 of a demihull from the geometry of its effective hull form, let us first 

 consider a two-dimensional, thin, symmetrical section. In a straight 



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